Ena spends all her income on her rent,travel and life expenses. She spends third of her income on rent,fifth of her income on travel ans 420$ on living expenses. How much does she make per month?

1. Denote Ena's monthly income by \( x \).

2. She spends one-third on rent:

\frac{x}{3}

3. She spends one-fifth on travel:

\frac{x}{5}

4. Total expenses on rent, travel, and living expenses:

\frac{x}{3} + \frac{x}{5} + 420

5. The total expenses are equals to her monthly income:

\frac{x}{3} + \frac{x}{5} + 420 = x

6. Find a common denominator for fractions:

\frac{5x}{15} + \frac{3x}{15} + 420 = x

7. Combine the fractions:

\frac{8x}{15} + 420 = x

8. Isolate \( x \) by moving \( \frac{8x}{15} \) to the right:

420 = x - \frac{8x}{15}

9. Simplify the right side:

420 = \frac{15x - 8x}{15}

10. Combine like terms:

420 = \frac{7x}{15}

11. Multiply both sides by 15:

420 \cdot 15 = 7x

12. Simplify:

6300 = 7x

13. Divide both sides by 7 to find \( x \):

x = \frac{6300}{7}

14. Simplify:

x = 900